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19147Re: [EMHL] Re: A Circle From Reflections In Incenter Cevians And Symmetries Of Vertices

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  • Quang Tuan Bui
    Aug 1, 2010
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      Dear Jean-Pierre,
      Thank you for interesting remark! It explains why a lot of central lines contain center T.
      Other than my quite complicated original construction, may be there are some elegant smart constructions for these six concyclic points?
      I am very happy if any one can find it!
      Thank you and best regards,
      Bui Quang Tuan

      --- On Sun, 8/1/10, jpehrmfr <jean-pierre.ehrmann@...> wrote:

      > From: jpehrmfr <jean-pierre.ehrmann@...>
      > Subject: [EMHL] Re: A Circle From Reflections In Incenter Cevians And Symmetries Of Vertices
      > To: Hyacinthos@yahoogroups.com
      > Date: Sunday, August 1, 2010, 9:17 PM

      > Dear Quang Tuan Bui
      > >
      > > It is interesting that these six points are concyclic
      > on one circle with center T.
      > > Barycentrics of T:
      > > a*(3*a*(a^2 - b^2 - c^2) - 2*(b + c)*(a - b + c)*(a +
      > b - c) + 4*a*b*c) : :
      > > Search value: +3.3876599710368
      >
      > We have IT = IO/3 Friendly. Jean-Pierre
      >
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